If the motor can be heard but the door stays in place, stop repeatedly operating it. A drive fault is one possibility, but the door and its connection need inspection too. Call with the opener model and a description of the sound you already noticed.
Avoid diagnosing by noise alone
A grinding sound does not identify a single replacement part. The technician needs to consider the drive, connection and load imposed by the door. Do not open the motor housing or run the opener with damaged lifting hardware to demonstrate the symptom.
Compare a defined repair with replacement
The useful comparison is an identified repair scope against a complete suitable replacement. Ask about part availability, the condition of the remaining unit and accessory compatibility. Retaining an opener makes sense only when the proposed work addresses the fault and allows appropriate checks afterward.
Your questions, answered.
Can a motor run even when the drive is damaged?
A sound from the unit does not prove that motion is being transferred to the door. Describe the behavior and arrange diagnosis.
Does this service include installing a new opener if needed?
We can discuss both options. A replacement is quoted separately after the existing system and your requirements are assessed.